The approach presented here is two-fold. On the one hand, previous analyses [1]}, [2]} get improved with the addition of new terms not considered before, and, on the other hand, the complete structures presented allow one to carry out a full comparison with the conventional chiral perturbation theory results by using the relations between the operator coefficients \(a_1\) , \(b_2\) , \(b_3\) , and \(c_3\)  and the \(SU(3)\)  invariants \(\mu _D\) , \(\mu _F\) , \(\mu _C\) , and \(\mu _T\) .
